Flower, 39, was chosen by new England coach Peter Moores and replaces Matthew Maynard with immediate effect.
"Andy will bring to the support staff a wealth of international experience as well as a clear understanding of the domestic game in England and Wales," Moores said.
"He has worked at the national academy for the past two seasons as a specialist batting coach and has done an excellent job. I am sure all the players will respond to his style and enjoy working with him."
Flower played 63 Tests between 1992 and 2002, scoring 4,794 runs at an average of 51.54.